Here are a few tips that will make searching for cartoon subjects easier.

Try typing a relevant word or words into the search box near the top right of the page.

This will display all cartoons that have those words associated with them.
Short versions of words will yield more results than long ones (i.e. cat will get more results rather cats - because the word cat is within the word cats but the word cats isn't within the word cat). Using several words will yield more targeted results (i.e. river bank will give results that contain both of the words river and bank and will thus tend to avoid showing you cartoons about the type of bank that deals with money.
Short words that are part of longer words will include results for the longer words too (i.e. car will include results for cartoon too, which covers just about every image on the site, so in cases like that it might be worth trying using longer words such as plurals - cars would avoid results for cartoon for instance).

Alternatively, click on the list of subjects in the row of topics near the top of the page.

These subjects include subcategories that open as drop-down lists when you place your cursor over them.
Clicking the main subject shows all of the cartoons in all of the subcategories - and any cartoons that aren't in subcategories.

Each cartoon has its categories displayed below the cartoon. Clicking on these categories will display all cartoons in that category.